MRF is an imaging technique that enables quantitative mapping of tissue or other material properties based on random or pseudorandom measurements of the subject or object being imaged. Examples of parameters that can be mapped include longitudinal relaxation time (T1), transverse relaxation time (T2), and spin or proton density (ρ), as well as experiment-specific parameters, such as off-resonance frequency. Advantageously, MRF provides a way to evaluate such parameters in a single, efficient imaging process. MRF is generally described in U.S. Pat. No. 8,723,518, which is herein incorporated by reference in its entirety.
The random or pseudorandom measurements obtained in MRF techniques are achieved by varying the acquisition parameters from one repetition time (“TR”) period to the next, which creates a time series of images with varying contrast. Examples of acquisition parameters that can be varied include flip angle, radio frequency (“RF”) pulse phase, TR, echo time (“TE”), and sampling patterns, such as by modifying one or more readout encoding gradients. Thus, the success of MRF is largely due to a specialized, incoherent acquisition scheme. More specifically, a sequence of randomized flip angles and repetition times (i.e., {(αm,TRm)}m=1M) is used to generate a sequence of images ({Im(x)}m=1M) with randomly varied contrast weightings, yielding incoherence in the temporal domain. Moreover, a set of highly undersampled variable density spiral trajectories can be used to acquire k-space data, which yields the spatial incoherence.
With these incoherently-sampled data, the conventional MRF reconstruction employs a simple template-matching procedure. Given a range of parameters of interest, the procedure uses a “dictionary” that contains all possible signal (or magnetization) evolutions simulated from the Bloch equation. That is, MRF matches an acquired magnetization signal to a pre-computed dictionary of signal evolutions, or templates, that have been generated from Bloch equation-based physics simulations (i.e., Bloch simulations). As a general example, a template signal evolution is chosen from the dictionary if it yields the maximum correlation with the observed signal for each voxel (extracted from the gridding reconstructions). The parameters for the tissue or other material in a given voxel are estimated to be the values that provide the best signal template matching. That is, the reconstructed parameters are assigned as those that generate the selected template.
Although the conventional MRF reconstruction procedures can be relatively robust in practice, there is no theoretic optimality associated with the reconstructed parameter maps. Furthermore, the original, straightforward template matching may not be computationally optimal, or even efficient. Recently, a number of new methods have been proposed to improve MRF reconstruction. Some have attempted to address the computational inefficiencies associated with the conventional MRF reconstruction. Others have proposed new iterative algorithms that leverage signal processing techniques, such as compressed sensing (“CS”), to improve the reconstruction accuracy. Despite these efforts, MRF reconstruction continues to be a challenge, particularly when a large number of tissue parameters are considered in an MRF process.